The invention is based on a windscreen wiper device of the type having at least one wiper arm that is driven by an electric motor whose rotary direction is variable at least in the extreme positions, with the electric power made available to the electric motor being reduced upon the change of rotary direction. From German Patent 29 44 224, a windscreen wiper device of this generic type is known that includes an electric motor whose direction of rotation can be varied in the extreme positions of a wiper arm. A pendulum gear, which produces a reciprocating motion from a rotary motion, can be dispensed with. The known device includes a drive stage that performs a reversal of the polarization of the electric motor operating voltage in the extreme positions. Imposing the full operating voltage on the electric motor that has come to a stop in the extreme positions leads to the occurrence of a starting current in the electric motor that is multiple times above the normal operating current. If the reversal of polarization of the electric motor takes place after the extreme position has been reached without any deceleration process, which is accomplished for instance by short-circuiting the electric motor, then the starting current can rise to twice the value, since the electromotive contrary force of the electric motor is added to the voltage of the energy source.